Robbie,
Sorry for the lag in response!
As implemented currently, the Egg doesn't do both at once. I don't think there's a reason why it couldn't but it would take some effort to refactor the software and I'm slightly afraid of it making online mode more fragile than it already is.
An off-the-shelf Power Bank USB battery (like you'd use for charging a phone) actually works a treat for the Egg. If you get the Offline Data Logging package installed, it comes with a coin cell already installed for the RTC Image may be NSFW.
Clik here to view.
Cheers,
Vic